220
G. W. BENSON AND F. C. TOMPKINS
specific effects is best deferred until measurements of some transport numbers in the sucrose solutions have been completed; this will make possible the examination of the effects on a single-ion basis. Some preliminary measurements on hydrochloric acid in 10% sucrose indicate a limiting conductiv-
Vol. 60
ity of about 357 ohm-' mole-' cm.2, corresponding to a ratio (A0 (sucrose)/ho (water)) of 0.838. It thus appears that the hydrogen ion is less retarded than other simple ions, which is consistent with the accepted view that it moves by an essentially different mechanism.
SORPTION OF AMMONIA BY DEHYDRATED POTASH ALUM BY G. W. BENSON' AND F. C. TOMPKINS Chemistry Department, Imperial College of Science and Technology, London, S.W. 7 Received J u l y id, 1866
The kinetics of sorption of ammonia by dehydrated potash alum crystals has been studied between 35.6 and 57.7" in the pressure range 1-30 cm. The amount sorbed a t constant pressure and temperature is a linear function of (t,ime)*/*but a process either of diffusion into non-interconnecting channels or of diffusion from a network of interconnecting channels into spherical zones has proved inadequate. A theory based on the presence of two different categories of sorption sites, and the replacement of residual water by ammonia molecules, however, has proved adequate in explaining the main experimental results.
Introduction Certain hydrated salts, on being heated in vucuo, lose all or part of their coordinated water molecules of hydration to give a skeleton lattice which collapses, either into an assembly of microcrystals with dimensions less than those necessary for an X-ray diffraction pattern, or into a highly disordered lattice of higher free energy than that of the corresponding microcrystalline farm.2 The structure of this product has a marked influence on the rate of dehydrationa of the parent hydrate since loss of water proceeds preferentially at the dehydration interface, consequently further information concerning the nature of the product would undoubtedly assist in our understanding of the dehydration process. The sorption of gases and vapors by the dehydrated solid has provided valuable data in the case of zeolites and clays4, but there have been few investigations of the ((simpler" dehydrated hydrates.6 The entropy and enthalpy of the transition of ('disordered" CuS04.H20 to the stable crystalline monohydrate has been investigated by Frost, e l uL6 Gar(1) Division of Mechanioal Engineering, National Research Council, Ottawa, Ontario. (2) G. B. Frost, K. A. Moon and E. H. Tompkins, Can. J . Chem., I S , 604 (1951): W. E. Garner and H. V . Pike, J . Chem. Soc., 1565 (1937). (3) J. A. Cooper and W. E. Garner, Trans. Faraday Soc.. 83, 1739 (1936). (4) R. M. Barrer, Proc. Roy. SOC.(London), 167, 392 (1938), R. M. Barrer and D. A. Ibbitson, Trans. Faraday Soc., 40, 195 (1944); R. M. Barrer, ibid., 40, 555 (1944); R. M. Barrer and D. A. Ibbitson, ibid., 40, 206 (1944): E. Rabinowitoh and C. Wood, ibid., 83, 947 (1936): A. B. Lamb and E. N. Ohl, J . A m . Cham. Soc., 67, 2154 (1935), A. B. Lamb and J. C. Woodliouse. ibid., 6 8 , 2637 (1936): M.G. Evans, Proc. Roy. Soc. (London). A134, 97 (1931); A. Tiaelius, 2. physik. Cham., A174, 401 (1935): T H l s JOURNAL, 40, 223 (1936): W. 0. Milligan and H. B. Weiser. ibid., 41, 1029 (1937): J. Mering, Trans. Faraday Soe., 4PB, 205 (1946); S. B. Hendrioks, I n d . Eng. Chsm., ST, 625 (1945); A. G. Keenan, R. W. Mooney and L. A. Wood, T H l s JOURNAL, 66, 1462 (1951). (6) G. B. Frost, K. A. Moon and E. H. Tompkins, Can. J . Cham., I S , 604 (1951); G. B. Frost and R. A. Campbell, ibid., 81, 107 (1953): H. W. Quinn, R. W. Missen and G. B. Frost, ibid., 88, 286 (1955); R. C. Wheeler and G. B. Frost, ibid., 58, 546 (1955); also Queen's University, Ontario, M.Sc., Theses by Moon (1948). Campbell (1950), Breck (1951), Missen (1951) and Wheeler (1951).
W.
ner, et aZ.,6have made detailed studies of the dehydration of alums, and Bielanski and Tompkins,' the sorption of water vapor by dehydrated potash alum. The latter authors concluded that the rate-controlling process was the diffusion of water molecules from higher adsorbed layers but could not accurately assess, by the weighing technique employed, the number of molecules in these layers. In the present work, the uptake of sorbate has been followed by measurement of the pressure of the gaseous adsorbate and many of the difficulties associated with the use of a sensitive spiral balance have been obviated. Experimental Materials.-Ammonia and sulfur dioxide were purified by repeated low tem erature vacuum distillation of the corresponding liquid o?commercial origin. Carbon monoxide was prepared from outgassed A.R. formic and sulfuric acids and passed through traps packed with glass wool and cooled in liquid nitrogen. A.R. potash alum was recrystallized from distilled water. Apparatus.-This was similar to that used previously* for obtaining sorption rates a t constant ressure except that constancy was maintained automaticalk by a relay operating a stopcocks which adjusted the mercury level in a calibrated gas buret. The sorption bulb, buret and connecting tubing were maintained a t constant temperature by water circulated from a thermostat. During the later stages of the investigation a constant volume apparatus was used; the rate process could be followed accurately over a few per cent. drop in total pressure so that measurements approximated t,o constant pressure conditions.
Results and Discussion Using conditions of dehydration similar to those employed previously,? viz., 16 hr. evacuation at 50", the amount of ammonia subsequently sorbed and its rate of sorption were irreproducible, but with single crystals of similar shape and weight, reproducibility (5%) was obtained either by increasing the time to 40 hr. or by raising the temperature to (6) J. A. Cooper and W. E. Garner, Trans. Faraday SOC.,82, 1739 (1936): J. A. Cooper and W. E. Garner, Proc. Roy. Soc. (London), AlT4, 487 (1940); G. P. Acock, W. E. Garner, J. Milstead and H. J. Willavoys, ibid.. 189, 508 (1947). (7) A. Bielanski and F. C. Tompkins, Trans. Faraday SOC.,46, 1072
(1950). ( 8 ) F. C. Tompkina. ibid.. 84, 1469 (1938). (9) D. M. Young, Chemistry and Industry, 155 (1948).
'
Feb., 1956
SORPTION OF AMMONIA
BY
DEHYDRATED POTASH ALUM
22 1
23.3 62' and evacuating for 16 hr. These more drastic conditions led to only a slight additional loss of water of hydration. As found previously,l nearly 2 13.5 moles of water per mole alum still remained in the crystal. After sorption of ammonia, the crystals were out5.7 gassed a t 62" for 16 hr., but in subsequent sorptions less ammonia was taken up, showing that the process is partly irreversible due, as shown later, to structural changes brought about in the dehydrated salt by the sorption process. Similarly, with crystals having similar geometric forms but of different weights, the plot of the rates of sorption against crystal weight showed considerable scatter, due to 2.55 slight variations of dehydration rates and in the degree of dehydration with crystal sizes. 1.15 Consequently, a master batch of small crystals was prepared so that each sample would be statistically the same. With such samples the plot of sorption rate against weight, although displaying little scatter, was not linear. This non-linearity is 1 2 3 4 5 6 7 8 undoubtedly associated with the fact that the deTime, in minutes'/*. hydration conditions cannot be maintained identiFig. 1.Sorption of ammonia at 57.7" at constant volume, cal with different masses (e.g., due to the presence plotted a~ a function of the square root of time: the mean af varying transient water vapor pressures, to pressure in cm. is indicated on each plot. different local rates of heating and degrees of selfcooling, etc. , fox the individual crystallites). likely that this model of non-connecting idealized Throughout, therefore, the same mass (0.1 g. for channels is correct. Alternatively, the channels may form an interconstant pressure, 1.0 g. for constant volume) of crystals was used and the dehydration carried out connecting network easily accessible to the ammoin the sorption bulb under the carefully controlled nia molecules, in which case some assumptions about the nature of the domains or zones within conditions given above. Sorption Rates.-The sorption rates at four tem- this network must be made. On a statistical basis, peratures, 35.6, 42.7, 50.1 and 57.7", were meas- the zones can be approximated by spheres particuured a t constant volume over the pressure range larly in view of Garner's work where spherical de0-30 cm. Some typical results a t 57.7' are shown hydration nuclki have been observed. To conin Fig. 1 where it is seen that the amount x of tinue quantitatively with the analysis, one must ammonia sorbed is a linear function of (time, t)'/* now either assume a size distribution of zones or a definite average radius of domains. A tractable after the first minute, i.e. €or diffusion of gas into these zones can be solution x = aP/z + b (1) obtained if the latter alternative is chosen. Using where a is the slope of the line and b the intercept spherical polar coordinates and assuming a constant on the x-ordinate. value for D, we may write Now it is likely that during dehydration a series of channels to the surface by and for the escape of water molecules are formed. If these channels are non-interconnecting then for a constant diffusion for t = 0,r < a, c = 0; and t > 0, T = u,c = co coefficient D and ''onedimensional" transport where a is the average radius of the zones, thesolualong the major axis of the channels, the amount tion has the form"J sorbed after a time will be given for long channels by
for t = 0, x > 0, c = 0; and t > 0, x = 0, c = co; J , is the flux a t x = 0. Equation 2 is thus consistent with the form of the experimental rate plots. The intercept of the et''* plot on the x-ordinate corresponds to a rapid initial adsorption on the external surface of the dehydrated crystal. With SO2 as adsorbate, a polar gas like NHI but larger in size, i t was found that the amount adsorbed in the same temperature range was, however, too small for accurate measurement and very much less than the b-values for ammonia. There was no rate procerjs so, presumably, the sorbed sulfur dioxide is largely confined to the small external surface area of the dehydrated alum. It seems therefore un-
-
and has been evaluated numerically by Benson. l 1 He finds that the amount sorbed is a linear function of (D&/a2)'/a over quite a wide range of f-values for small (D?r2t/uz)'/*;this model is therefore also consistent with the experimental results. On this theory a considerable internal surface should be easily accessible to small molecules, such as CO. We have, therefore measured the adsorption of this gas a t liquid-air temperature and obt.ained a normal (type 11) B.E.T. isotherm (Fig. 2) from which a surface area of 5 m.2 per g. adsorbent was evaluated. No rate process subsequent to the (IO) H. 8. Carslaw and J. C. Jaeger, "Heat Conduction in Solids," Clarendon Preas, Oxford, 1947. (11) G . W. Benaon, Ph.D. The&, London University. 1962.
G. W. BENSON AND F. C. TOMPKINS
222
5 16 14 1
z
12
3 rn
8 10 2
8
b “06
6
$ 4
.I
+a
$ 2 (R
visualize the building-up of higher layers (multilayer formation) with an accompanying small monotonic increase in concentration in the first layer, so that despite the lar e increase in the total amount adsorbed, the rate o sorption increases only slightly and the rate against pressure plot shows no singularity. Nevertheless this theory is difficult to accept for the following reasons: (i) The large abrupt increase in the value of the intercept b occurs (cf. Fig. 3) when a critical amount (0.3 mole/mole adsorbent) is adsorbed and this is independent of the pressure or the temperature. (ii) The plot of the total amount sorbed at the completion of the rate process (Fig. 4) shows no similar large increase as might be expected were multilayer formation taking place.
f
Pressure, cm. Fig. 2.-Adsorption isotherm for CO a t -196”
initial adsorption was found and the monolayer capacity per g. adsorbent was independent of the weight of dehydrated alum (cf. the non-linearity of the rate against weight plot using ammonia). This large internal area, easily accessible at liquid-air temperature by small molecules, is consistent with the zone theory. Such zones, assumed spherical a%d of equal size, would have a radius of about 3000 A. to give a surface area of 5 m.z. On this view the intercept b on the rate curves (Fig. 1) for various constant pressures and constant temperature represents the amount of ammonia rapidly adsorbed on the internal surfaces for various equilibrium pressures. Such “isotherms” at four different temperatures are plotted in Fig. 3. They resemble type V B.E.T. plots where the sharp increase of amount sorbed over a small pressure range is ascribed to the filling of pores and capillaries of the dehydrated alum.
Vol. 60
v
E
I
I
I
2
4
6
Fig. 4.-Total
I
I
.
n
u
I
I
I
I
I
I
I
8 10 12 14 16 18 20 22 24 Pressure, cm. sorption at 50.1” as a function of pressure.
(iii) If the area deduced from the B.E.T. isotherm for CO is accepted, viz., 5 m.z/g., then the amount of ammonia sorbed on the internal surfaces at the critical value (0.3 mole/mole) corresponds to 6 layers and above the critical b value to nearly 50 layers. In view of the non-penetration of the sulfur dioxide molecule under comparable conditions of temperature and pressure, channels sufficiently wide for such a thick layer cannot be present. (iv) If Fig. 3 represents a series of reversible adsorption isotherms then the “critical” pressure should increase with temperature. The reverse however is found. I4 Any theory based on an ortho2 0 dox diffusion phenomenon thus b 2.0 seems improbableunless one pos8 tulates adiffusion coefficient that d varies extremely rapidly with concentration in the initial stages. Concept of DifIerent Sorption m 1.0 3 Sites.-& alternative theory involving the concept of different 3 atypes of sorption sites, however, is consistent with the experimental results. From previous work on dehydrated salts of similar 2 4 6 8 10 12 14 16 18 zo 22 24 type to potash alum, the dehyPressure, om. drated product often comprises Fig. 3.-Variation of the intercept b with teomperature and pressure: 0,35.6”; XI a large number of small crystal42.7”; 0 ,50.1 ; 0,57.7”. l i e domains in a fairly open Now it is reasonable to assume on the zone model matrix of non-crystalline, collapsed, disordered that the rate of sorption is a function of the con- material. There are likely to be many different centration of ammonia molecules in the first layer sites for ammonia attachment where the energy at the surface of the zones. One can therefore of binding of the sorbate molecule varies with
-
-. .I
1
SORPT~ON OF AMMONIA BY DEHYDRATED POTASH ALUM
Feb., 1956
the nature of the site. For simplicity, these sites are assumed to comprise two main categories which we shall refer t o as crystalline and amorphous sites, without implying more than that these regions differ in degree of order and therefore in the sorption energy of the sites. We recall that about 2 moles of water per mole alum still remain in the dehydration product but that under more drastic conditions these can eventually be removed. We denote sites in the amorphous material by X, and those in the crystalline material by Y; each type is in equilibrium with the same very small vapor pressure of water, Le. X Y
+ Hz0 I ’ X.Hz0, K I + HzO Y.HzO, Kz
or, combining Y
+ X.Hz0
X
+ Y.Hz0,
(3) (4)
K = Kz/Ki ( 5 )
The constant K I is assumed large compared with K z , i.e., K is small and the binding energy for HzO at the X sites is greater than.that at the Y sites; the hydration of the amorph6us sites is therefore favored. The sorption of ammonia is therefore largely associated with the X-sites, which process disturbs the equilibrium in that more X sites are made available as sorption proceeds. At time t = 0 let: t o = the number of X sites available for adsorption, N = the number of X.HzO sites, the units being in terms of “moles” per mole of alum. At time “t” let: x = number of X sites occupied by sorbed NH, molecules, 5 = number of free X sites. Equilibrium (5) is assumed to be maintained during the rate process so that
if [Y1 is sufficiently large variations in its value will have little influence on K so that it is permissible to write
+ E - Eo) - z - E + Eo) rearranging E’ + + K’ - 4c)E - K’(N + 40 - X ) = 0 K’ = K [ Y ] =
€(X
(N
(5
(6)
processes are measured under effectively constant pressure conditions. From equations 8 and 9
which, on integration, gives x
”\ = -kK‘t
+ ( N + K ’ ) log
(11)
The rate of sorption will initially be large compared with the rate of the forward reaction of the equilibrium (5), so that the equilibrium is displaced and equation 11 is invalid. However, as sorption proceeds, the number of available X sites decreases until the rate of sorption is small compared with the rate of attainment of the equilibrium and the above analysis is now valid. We denote the value of 50 a t the new origin of time (to) by io’. At this time the value of to’is small compared with N , consequently since K’ is also small, equation 11takes the form X’
3< .
> 5 31 [ ( t o - K’ - x) f [YH20], both [XI and [YHZO] are small compared with [X.HZO],the assumptions to’
